Another commonly studied network is Zachary's karate club [1]}, a social network split into two communities due to a dispute between the club's instructor (node 1) and president (node 34). Using \(N_B=2\)  recovers the usual two community pattern, Figure REF  shows results for \(N_B = \lbrace 3,6\rbrace \) . These values are chosen because they seem to be local minima of sorts, the optima for \(N_B = \lbrace 4,7\rbrace \)  only use 3 and 6 communities respectively. Slightly higher \(Q(B)\)  can be obtained for \(N_B \ge 8\)  but there is a balance to strike between optimisation and interpretability of the block matrix.
